1. **State the problem:** Solve the quadratic equation $$x^2 - x - 42 = 0$$ by factoring. 2. **Recall the factoring method:** To factor a quadratic equation of the form $$ax^2 + bx + c = 0$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = -1$$, and $$c = -42$$. 4. **Find two numbers:** We need two numbers that multiply to $$1 \times (-42) = -42$$ and add to $$-1$$. These numbers are $$6$$ and $$-7$$ because $$6 \times (-7) = -42$$ and $$6 + (-7) = -1$$. 5. **Rewrite the middle term:** Rewrite $$-x$$ as $$6x - 7x$$: $$x^2 + 6x - 7x - 42 = 0$$ 6. **Group terms:** $$(x^2 + 6x) - (7x + 42) = 0$$ 7. **Factor each group:** $$x(x + 6) - 7(x + 6) = 0$$ 8. **Factor out the common binomial:** $$(x - 7)(x + 6) = 0$$ 9. **Set each factor equal to zero:** $$x - 7 = 0 \quad \text{or} \quad x + 6 = 0$$ 10. **Solve for $$x$$:** $$x = 7 \quad \text{or} \quad x = -6$$ **Final answer:** The solutions to the equation $$x^2 - x - 42 = 0$$ are $$x = 7$$ and $$x = -6$$.